A generalized global Arnoldi method for ill-posed matrix equations

Authors:
A. Bouhamidi;K. Jbilou;L. Reichel;H. Sadok
Affiliations:
Université de Lille Nord de France, L.M.P.A, ULCO, 50 rue F. Buisson BP699, F-62228 Calais-Cedex, France;Université de Lille Nord de France, L.M.P.A, ULCO, 50 rue F. Buisson BP699, F-62228 Calais-Cedex, France;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;Université de Lille Nord de France, L.M.P.A, ULCO, 50 rue F. Buisson BP699, F-62228 Calais-Cedex, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 9
Cited 0

Topics in matrix analysis

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Abstract

This paper discusses the solution of large-scale linear discrete ill-posed problems with a noise-contaminated right-hand side. Tikhonov regularization is used to reduce the influence of the noise on the computed approximate solution. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a generalized global Arnoldi method, that respects the structure of the equation, for the solution of the regularized problem. Theoretical properties of the method are shown and applications to image deblurring are described.